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We apply the method of holographic renormalization to computing black hole masses in asymptotically anti-de Sitter spaces. In particular, we demonstrate that the Hamilton-Jacobi approach to obtaining the boundary action yields a set of counterterms sufficient to render the masses finite for four, five, six and seven-dimensional R-charged black holes in gauged supergravities. In addition, we prove that the familiar black hole thermodynamical expressions and in particular the first law continues to holds in general in the presence of arbitrary matter couplings to gravity.
In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow coincides wi
Recently, a practical approach to holographic renormalization has been developed based on the Hamilton-Jacobi formulation. Using a simple Einstein-scalar theory, we clarify that this approach does not conflict with the Hamiltonian constraint as it se
We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is
We examine the real-time dynamics of a system of one or more black holes interacting with long wavelength gravitational fields. We find that the (classical) renormalizability of the effective field theory that describes this system necessitates the i
In holographic inflation, the $4D$ cosmological dynamics is postulated to be dual to the renormalization group flow of a $3D$ Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory ---in which inf